RPSC Assistant Professor 8th Oct 2021 Economics Paper 2 (Previous Year Paper)

The correct answer is: Contributes around 16% GVA while it employs around 43% of workforce.

Key Points

• Primary Sector in India
• The primary sector includes agriculture and mining activities.
• According to the Periodic Labour Force Survey (PLFS) 2018-19, this sector contributes around 16% of the Gross Value Added (GVA) to the economy.
• Despite its significant contribution to employment, it employs approximately 43% of the workforce.
• This indicates a high dependency on agriculture and mining for employment in India.

Additional Information

• Economic Contribution
• The Gross Value Added (GVA) is a measure of the value of goods and services produced in an area, industry, or sector of an economy.
• A higher percentage of employment in the primary sector compared to its GVA contribution indicates lower productivity in this sector.
• This is a common characteristic of developing economies where a large portion of the population is engaged in agriculture with relatively low output per worker.
• Employment Statistics
• The primary sector’s employment statistics highlight the need for diversification and development of other sectors like manufacturing and services to reduce dependency on agriculture.
• Efforts to improve productivity and income in the agricultural sector can help in better economic balance.
• Incorrect Options
• The other options provided incorrect statistics regarding the GVA contribution and workforce employment percentages.
• For example, a GVA of 14%, 12%, or 18% with higher employment percentages does not accurately represent the data from the Periodic Labour Force Survey 2018-19.

The correct answer is - (B) and (C) only

Key Points

• Inclusive Growth
• Inclusive growth refers to an economic growth strategy that ensures equitable opportunities for all members of society, particularly the marginalized and disadvantaged groups.
• It aims to reduce poverty, enhance social inclusion, and create employment opportunities.
• Strengthened Fiscal Policies
• Strengthened fiscal policies help in redistributing income and wealth, thereby promoting economic equality.
• Such policies include progressive taxation, increased public expenditure on social services, and targeted subsidies.
• Increased Transparency
• Increased transparency in governance and business practices ensures that resources are allocated efficiently and corruption is minimized.
• Transparency helps in building trust among citizens and encourages their participation in the economic process.

Additional Information

• Creation of a Controlled Environment by the Government
• While government intervention is necessary, an overly controlled environment can stifle innovation and entrepreneurship, which are crucial for inclusive growth.
• Complete Ban on FDI
• A complete ban on Foreign Direct Investment (FDI) can limit the inflow of capital, technology, and expertise, which are essential for economic growth and development.
• FDI can create jobs, enhance productivity, and integrate domestic markets with global markets.

The correct answer is - 1995-96 to enhance public sector capital formation in rural areas.

Key Points

• Rural Infrastructure Development Fund (RIDF)
• The RIDF was established in 1995-96 by the Government of India.
• The primary objective was to enhance public sector capital formation in rural areas.
• It was set up to provide loans to State Governments and State-owned corporations for the completion of ongoing projects related to rural infrastructure.
• The National Bank for Agriculture and Rural Development (NABARD) manages the RIDF.

Additional Information

• Other Options
• 2000-01 to enhance private sector capital formation in rural areas: This option is incorrect because the RIDF was not established for private sector capital formation, and the year mentioned is incorrect.
• 2004-05 to enhance public sector capital formation in rural areas: This is incorrect because the RIDF was established earlier, in 1995-96.
• 1996-97 to enhance private sector capital formation in rural areas: This is incorrect as the RIDF was focused on public sector projects and was established a year earlier.

The correct answer is - 1965-66, 1971-72, 1979-80

Key Points

• Contraction in Indian GDP
• The National Statistical Office (NSO) has estimated a contraction of real GDP by 7.7% in 2020-21.
• This is the fourth contraction in India's GDP since 1960-61.
• The previous three contractions occurred in the years 1965-66, 1971-72, and 1979-80.
• These years were marked by significant economic and political challenges in India.

Additional Information

• 1965-66
• This period was marked by the Indo-Pakistan war, which had significant economic repercussions.
• There were also widespread droughts leading to agricultural distress.
• 1971-72
• The economy faced challenges due to the Indo-Pakistan war leading to the creation of Bangladesh.
• There was also global economic instability during this period.
• 1979-80
• This period saw global oil crises which significantly impacted India's economy.
• There were also internal political uncertainties and policy challenges.
• Other Options
• Options such as 1969-70, 1970-71, 1980-81, and others listed in the incorrect options did not align with the historical records of GDP contraction in India.
• These years might have had economic difficulties but did not record the same level of contraction as the correct years.

The correct answer is - Bharatmala Pariyojana

Key Points

• Bharatmala Pariyojana
• Bharatmala Pariyojana is an umbrella program for the highways sector in India.
• It aims to build more than 80,000 kilometers of roads, highways, greenfield expressways, and bridges.
• The program involves an investment of 107 billion dollars to improve road connectivity across the country.
• The initiative focuses on optimizing the efficiency of the movement of goods and people by bridging critical infrastructure gaps.

Additional Information

• Sagarmala Project
• The Sagarmala Project aims to promote port-led development in India.
• It focuses on improving the efficiency of ports, enhancing port connectivity, and promoting the development of coastal communities.
• The project seeks to boost merchandise exports and create jobs in the logistics sector.
• Dedicated Freight Corridor
• The Dedicated Freight Corridor is a railway project aimed at creating freight-specific rail lines.
• It is designed to decongest the existing railway network and enhance the movement of goods.
• The project includes the development of both the Eastern and Western corridors.
• Multimodal Logistics Park
• Multimodal Logistics Parks are designed to reduce logistics costs and improve supply chain efficiency.
• These parks integrate various modes of transport like road, rail, and air to facilitate the smooth movement of goods.
• They include facilities such as warehousing, cold storage, and container terminals.

The correct answer is - Only (B) is correct.

Key Points

• Statement Analysis:
• Statement (A): During the WTO TRIPS council meeting held on 15-16 October, 2020, India and South Africa (not the US) jointly proposed a waiver from certain provisions of the TRIPS Agreement for the prevention, containment, and treatment of Covid-19.
• Statement (B): The proposal aimed to ensure that intellectual property rights do not become a barrier to the timely and affordable access to medical products needed to combat Covid-19.

Additional Information

• WTO TRIPS Agreement:
• The TRIPS (Trade-Related Aspects of Intellectual Property Rights) Agreement is a legal agreement between all the member nations of the World Trade Organization (WTO).
• It sets down minimum standards for many forms of intellectual property regulation, as applied to nationals of other WTO members.
• Covid-19 and Intellectual Property:
• The Covid-19 pandemic highlighted the need for global access to medical products, including vaccines, diagnostics, and therapeutics.
• Intellectual property rights can sometimes pose challenges to widespread and equitable access to these essential medical products.
• India-South Africa Proposal:
• On 2 October 2020, India and South Africa submitted a proposal to the WTO TRIPS Council for a temporary waiver of certain provisions of the TRIPS Agreement for the prevention, containment, and treatment of Covid-19.
• The proposal was to allow countries to not grant or enforce patents and other intellectual property rights related to Covid-19 products until global herd immunity is achieved.

The correct answer is - 68th

Key Points

• India's rank in trading across borders parameter on 'Ease of Doing Business' Index improved from 146 in 2018 to 68th in 2020.
• This significant improvement highlights the efforts made by the Indian government to streamline and simplify the process of trading across borders.
• Factors contributing to this improvement include the introduction of electronic sealing of containers, upgrading of port infrastructure, and the implementation of a single window for customs clearance.

Additional Information

• Overview of Other Options:
• 70th: While a significant improvement, it is not as substantial as moving to the 68th rank.
• 60th: This would indicate an even more remarkable improvement, but it is not the rank India achieved in 2020.
• 50th: This is an even more ambitious rank, reflecting a higher level of ease in trading across borders, but it was not the rank achieved by India in 2020.

The correct answer is - 3 %

Key Points

• 3 %
• The percentage of total imports accounted for by computer hardware and peripherals during April-November 2020 is 3%.
• This calculation is based on the available import data for the specified period.
• The value 3% indicates that out of the total imports, computer hardware and peripherals made up a very small fraction.

The correct answer is - 14th

Key Points

• Indian Pharmaceutical Industry
• The Indian pharmaceutical industry occupies the 14th position in the world in terms of value.
• India is a significant player in the global pharmaceutical sector, known for its high-quality generic medicines.
• The industry is known for its large volume of production, being the 3rd largest in the world by volume.
• India supplies over 50% of the global demand for various vaccines and 40% of the generic demand in the United States.

Additional Information

• Global Pharmaceutical Industry
• The global pharmaceutical industry is vast and diverse, with many countries contributing significantly to research, development, and production.
• The United States, China, and Japan are among the top countries in terms of pharmaceutical market value.
• India's focus on generic medicines has allowed it to capture a significant share of the global market, especially in developing countries.
• The Indian pharmaceutical sector is also a major supplier to international organizations like the World Health Organization (WHO).

The correct answer is - Malaysia

Key Points

• Malaysia
• In the period of April-November 2020, Malaysia emerged as one of the top 10 export destinations for India, showing significant growth in trade relations.
• This was in contrast to the previous year (April-November 2019), where Malaysia did not feature in the top 10 export destinations.
• The inclusion of Malaysia indicates a strengthening economic partnership and increased demand for Indian goods in the Malaysian market.
• Key export commodities to Malaysia included refined petroleum, organic chemicals, and machinery.

Additional Information

• Germany
• Germany has consistently been one of India's top export destinations for several years, known for importing goods such as textiles, chemicals, and machinery from India.
• The robust trade relations between India and Germany have been long-standing, driven by industrial and technological exchanges.
• Nepal
• Nepal is a neighboring country with strong trade ties with India, importing a variety of goods including petroleum products, machinery, and pharmaceuticals.
• The geographic proximity and cultural ties contribute to the steady trade relationship between the two nations.
• Netherlands
• The Netherlands is a significant European trade partner for India, importing goods such as machinery, textiles, and chemicals.
• Trade relations with the Netherlands have been stable, with the country consistently featuring among the top export destinations for India.

The correct answer is - Drug formulations and Biologicals

Key Points

• Drug formulations and Biologicals
• This category includes various pharmaceutical products such as vaccines, medicinal preparations, and bio-pharmaceuticals.
• During the period of 2020-21 (April-November), there was a significant increase in demand for these products globally due to the COVID-19 pandemic.
• India, being one of the largest producers of generic drugs and vaccines, saw a favorable trade balance in this category.
• The increased exports of COVID-19 related medications and biological products contributed to the positive trade balance.

Additional Information

• Electronic Components
• Electronic components include items such as semiconductors, capacitors, and resistors.
• India imports a significant amount of these components, leading to a trade deficit in this category.
• Despite growth in the electronics manufacturing sector, dependency on imports remained high.
• Vegetable Oil
• India is one of the largest importers of vegetable oil, including palm oil, soybean oil, and sunflower oil.
• The country relies heavily on imports to meet its domestic demand, resulting in a trade deficit in this commodity.
• Fertilizers Manufactured
• India imports a substantial amount of fertilizers to support its agricultural sector.
• The dependency on imports for various fertilizers like urea, DAP (Di-ammonium Phosphate), and others leads to a trade deficit in this category.

The correct answer is - USA followed by Bangladesh and Nepal

Key Points

• India's Merchandise Trade Balance
• Trade balance refers to the difference between a country's exports and imports of goods.
• A favorable trade balance indicates that a country exports more than it imports, leading to a trade surplus.
• For the period 2020-21 (April - November) compared to 2019-20 (April - November), India had the most favorable trade balance with the USA, followed by Bangladesh and Nepal.
• This means that India exported more goods to these countries than it imported from them during the specified period.

Additional Information

• China, UK, The Netherlands
• China is one of India's largest trading partners, but the trade balance is usually unfavorable for India due to high imports from China.
• The UK and The Netherlands are significant trading partners, but they do not top the list in terms of favorable trade balance for the specified period.
• Saudi Arabia, UK, The Netherlands
• Saudi Arabia is a major exporter of crude oil to India, leading to a generally unfavorable trade balance for India.
• While the UK and The Netherlands are important partners, they do not lead in terms of favorable trade balance for the specified period.

The correct answer is - ₹12,000 Crores

Key Points

• ₹12,000 Crores
• During the financial year 2020-21, under the 'Scheme for Special Assistance to States for Capital Expenditure,' the central government of India provided special financial assistance to state governments.
• This assistance was in the form of a 50-year interest-free loan, which is a significant fiscal support measure aimed at boosting state capital expenditure.
• The total sum allocated for this scheme was ₹12,000 Crores.
• This financial assistance was intended to spur economic growth and development by enabling states to invest in critical infrastructure projects.

Additional Information

• ₹10,000 Crores
• This figure is incorrect as it is lower than the actual allocated amount.
• While ₹10,000 Crores is a substantial amount, the correct allocation was higher.
• ₹14,000 Crores
• This figure is incorrect as it exceeds the actual allocated amount.
• While capital expenditure could benefit from higher allocations, the designated sum for this specific scheme was lower.
• ₹8,000 Crores
• This figure is incorrect as it is significantly lower than the actual allocated amount.
• The correct figure is higher to ensure substantial capital investment by states.

The correct answer is - 10

Key Points

• One Nation One Ration Card System
• The 'One Nation One Ration Card' (ONORC) system is an initiative by the Government of India to ensure food security for all citizens across the country.
• It allows beneficiaries to receive their entitled food grains from any Fair Price Shop (FPS) in the country using their existing ration card.
• The system aims to provide seamless access to subsidized food grains to migrant workers and their families.
• As of 30 December 2020, a total of 10 states had successfully implemented the ONORC system.

Additional Information

• Other Options:
• 14 States: This number is higher than the actual count of states implementing ONORC by the end of December 2020.
• 12 States: This number is slightly higher than the actual count, but still incorrect.
• 8 States: This number is lower than the actual count, making it incorrect as well.
• Implementation Progress
• The ONORC system was launched in 2019 and aims to cover all states and Union Territories by March 2021.
• It is part of the government's larger plan to ensure food security and mitigate hunger across the country, especially for migrant populations.
• Benefits of ONORC
• Ensures no beneficiary is deprived of their food security entitlements.
• Allows ease of access to food grains from any FPS across the country.
• Supports the government's vision of 'One Nation, One Market' by integrating various state-level Public Distribution Systems (PDS).

The correct answer is - 3.5% of GDP

Key Points

• Medium Term Fiscal Policy Statement
• The Medium Term Fiscal Policy Statement (MTFPS) is a document presented along with the Union Budget in India.
• It outlines the government's fiscal policy and targets for the medium term, typically covering a period of three years.
• The MTFPS is part of the Fiscal Responsibility and Budget Management (FRBM) Act, which aims to ensure fiscal discipline and transparency in the country's budgetary process.
• Fiscal Deficit Target for FY 2020-21
• The fiscal deficit is the difference between the government's total expenditure and its total revenue (excluding borrowings).
• For the financial year 2020-21, the MTFPS presented with the Union Budget pegged the fiscal deficit target at 3.5% of GDP.
• This target is an indication of the government's borrowing requirement for that fiscal year to meet its expenditure commitments.

Additional Information

• Option 1 - 2.5% of GDP
• This figure is significantly lower than the actual fiscal deficit target set for FY 2020-21, indicating a much more conservative borrowing stance.
• Option 3 - 3% of GDP
• This target was relevant for previous years as per the FRBM Act, but it was revised for FY 2020-21 due to various economic factors including the impact of the COVID-19 pandemic.
• Option 4 - 4% of GDP
• This figure is higher than the actual target set, reflecting a more expansive fiscal policy stance than what was officially adopted.

The correct answer is - 1% of GDP

Key Points

• Non-debt capital receipts in 2020-21
• The non-debt capital receipts for the fiscal year 2020-21 have been pegged at 2.3 lakh crores.
• These receipts include disinvestment proceeds, recovery of loans, and other forms of capital income that do not increase the debt liability of the government.
• Non-debt receipts are important for funding capital expenditures without adding to the debt burden.
• 1% of GDP
• The figure of 2.3 lakh crores as non-debt capital receipts is approximately 1% of India's Gross Domestic Product (GDP) for the fiscal year 2020-21.
• GDP is a monetary measure of the market value of all final goods and services produced in a specific time period, which provides an overall economic snapshot.
• This percentage indicates the proportion of the country's total economic output represented by these non-debt capital receipts.

Additional Information

• 0.5% of GDP
• If the non-debt capital receipts were 0.5% of GDP, it would imply a significantly lower figure compared to 2.3 lakh crores.
• This would mean the government's non-debt receipts are a smaller fraction of the economic output.
• 0.75% of GDP
• A figure of 0.75% of GDP would also indicate a lower amount of non-debt capital receipts than 2.3 lakh crores.
• Such a percentage would reflect a moderate but still lower proportion of the GDP.
• 1.5% of GDP
• If non-debt capital receipts were 1.5% of GDP, it would suggest a higher figure than 2.3 lakh crores.
• This would represent a larger share of the national economic output being derived from non-debt sources.

The correct answer is - 26 %

Key Points

• • As per the 2019-20 Provisional Accounts (PA), the interest payments as a percentage of total revenue expenditure accounted for 0.26.
• This indicates that out of the total revenue expenditure, 26% was spent on paying interest.
• Interest payments are a significant portion of the government's expenditure, and keeping track of this percentage helps in understanding the fiscal health of the government.

The correct answer is - Income Tax Department Charter

Key Points

• Honoring the Honest Platform
• Launched in August 2020 by the Government of India as a part of tax administration reform.
• Aim is to make tax systems more transparent, efficient, and taxpayer-friendly.
• Focuses on minimizing direct interaction between taxpayers and tax authorities.
• Faceless Assessment
• This initiative aims to eliminate the need for face-to-face interactions between taxpayers and tax officers.
• Reduces chances of corruption and ensures uniformity in tax assessments.
• Faceless Appeal
• Provides for the elimination of physical interface between the taxpayer and the tax authorities during the appeal process.
• Ensures transparency, efficiency, and accountability in the tax appeal process.
• Tax Payer's Charter
• Defines the rights and duties of taxpayers.
• Aims to build trust between taxpayers and the administration.
• Seeks to enhance the efficiency of the tax system.

Additional Information

• Faceless Tax Administration
• Part of the broader "Transparent Taxation" initiative.
• Aims to reduce human discretion in tax administration and improve efficiency.
• Uses technology to handle tax-related processes and grievances.
• Income Tax Department
• The statutory body responsible for the administration of direct tax laws in India.
• It comes under the Department of Revenue, Ministry of Finance.
• While it plays a crucial role in tax administration, it does not constitute a charter as mentioned in the options.

The correct answer is - IT services

Key Points

• IT services
• The IT services subsector includes consulting, systems integration, IT outsourcing, and managed services.
• In 2019-20, IT services held the largest share of the IT-BPM sector's revenue, constituting over 50%.
• This dominance is attributed to the global demand for digital transformation, cloud computing, and cybersecurity services.
• Indian IT services companies like TCS, Infosys, and Wipro have been leading this charge, providing end-to-end solutions to global clients.

Additional Information

• Software products and engineering services
• This subsector includes the development of software products, engineering services, and R&D services.
• Although growing, it did not constitute the majority share in 2019-20.
• Hardware
• This involves the manufacturing and sale of physical computer components and devices.
• Hardware has a smaller share compared to IT services and software products.
• BPM (Business Process Management)
• This subsector includes services like customer support, finance and accounting, and human resource management.
• While significant, BPM did not constitute the majority share in the IT-BPM sector's revenue in 2019-20.

The correct answer is - UK

Key Points

• UK
• The UK was the second largest export market for IT-BPM services from India in the fiscal year 2019-20 in terms of export earnings.
• India's IT-BPM (Information Technology and Business Process Management) sector has historically had strong ties with the UK market.
• The robust demand for IT services in the UK is driven by its mature market and the need for digital transformation across various industries.

Additional Information

• USA
• The USA is the largest export market for Indian IT-BPM services, not the second largest.
• Indian IT companies have a significant presence in the USA, providing a wide range of services from software development to consulting.
• Europe (excluding UK)
• Europe (excluding UK) comprises several countries with varying levels of demand for IT services.
• While Europe is a major market, it collectively does not surpass the UK's position as the second largest individual market.
• Asia Pacific
• The Asia Pacific region, including countries like Australia, Japan, and Singapore, is a growing market for Indian IT services.
• However, it does not yet surpass the UK in terms of export earnings from IT-BPM services.

The correct answer is: 8.8%.

The expenditure on social services, which includes areas like education, health, and social welfare, is a critical indicator of a country's commitment to human development and social infrastructure. During the period from 2014-15 to 2020-21 (BE), the combined expenditure by the central and state governments in India as a proportion of GDP showed a significant increase, reflecting an enhanced focus on social sector development.

Key Points

• Growth in Expenditure:
• During the 2014-15 period, the combined expenditure on social services by the central and state governments was 6.2% of GDP.
• By the 2020-21 Budget Estimate (BE), this expenditure rose to 8.8% of GDP, showing a consistent increase over the years.
• Major Areas of Spending:
• Education: The largest component of social service expenditure, aimed at improving literacy and skills.
• Health: Enhanced focus on healthcare infrastructure, public health schemes, and pandemic-related spending.
• Social Welfare: Schemes targeting vulnerable populations, including women, children, and senior citizens.
• Government Initiatives:
• Introduction of schemes like Ayushman Bharat for health and Samagra Shiksha for education contributed significantly to the increase in spending.
• Efforts to address socio-economic inequalities through direct benefit transfers and rural employment schemes also played a role.

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The correct answer is: 26.5%.

The expenditure on social services as a percentage of total government expenditure represents the priority given to sectors such as education, health, and social welfare. In 2020-21 (BE), this share reached a significant 26.5%, reflecting the government's emphasis on social development and welfare initiatives, especially during a challenging fiscal period.

Key Points

• Increased Share of Social Services:
• In 2020-21 (BE), the allocation for social services rose to 26.5% of the total government expenditure.
• This increase is attributed to the heightened need for investment in health and social welfare due to the COVID-19 pandemic.
• Main Sectors Benefiting:
• Health and Family Welfare: Significant funding for pandemic-related healthcare infrastructure and vaccination programs.
• Education: Continued focus on digital learning initiatives and infrastructure development in schools and colleges.
• Social Welfare: Increased expenditure on schemes supporting vulnerable populations, including food security programs and employment generation.
• Comparison with Previous Years:
• The share of social services expenditure has consistently increased over the years, showcasing the government's commitment to inclusive development.
• In earlier years, the share hovered around 22–23%, highlighting the progressive rise in focus.

Additional Information

• Importance of Social Sector Spending:
• Allocations to social services are essential for reducing inequalities and enhancing human capital development.
• This expenditure directly impacts the quality of life and socio-economic opportunities for citizens.
• Government Initiatives:
• Flagship schemes like Ayushman Bharat, MGNREGA, and Samagra Shiksha have contributed to this increased allocation.
• Special focus on healthcare and employment generation reflects the government's response to the pandemic's economic and health challenges.
• Future Outlook:
• Maintaining or increasing the share of social services expenditure is critical for achieving Sustainable Development Goals (SDGs).
• Ensuring efficient implementation and targeted spending will maximize the impact of these allocations.

The correct answer is - Enable every household get assured supply of potable piped water

Key Points

• Enable every household get assured supply of potable piped water
• This statement is not true regarding Jal Jeevan Mission.
• Jal Jeevan Mission aims to provide a functional tap water connection to every rural household, but it does not assure an uninterrupted supply of potable piped water.
• The mission focuses on infrastructure creation rather than guaranteeing a continuous supply.

Additional Information

• Jal Jeevan Mission Overview
• Launched by the Government of India in 2019.
• Aims to provide functional tap water connection to every rural household by 2024.
• Focuses on building infrastructure for water supply systems.
• Emphasizes on community-managed and demand-driven approaches for sustainable water supply.
• Community Managed Programme
• The mission encourages community participation in planning, implementation, and management of water supply infrastructure.
• Local communities are trained and empowered to manage their water resources effectively.
• Demand Driven Programme
• The programme is designed to be responsive to the needs and demands of the local population.
• Ensures that water supply schemes are implemented based on actual requirements and preferences of the communities.

The correct answer is - The number of minimum wage rate would be around ₹ 200 in entire country as against 10,000 at present.

Key Points

• The number of minimum wage rate would be around ₹ 200 in entire country as against 10,000 at present.
• This statement is incorrect because the Code of Wages, 2019 does not specify that the minimum wage rate would be around ₹ 200 for the entire country.
• The Code of Wages aims to simplify and rationalize the minimum wage structure, not standardize it to such a low amount.

Additional Information

• Revision of minimum wages every 5 years
• This is a correct statement as the Code of Wages, 2019 mandates the revision of minimum wages every five years to ensure that wages keep pace with changes in living conditions and inflation.
• A statutory concept of floor wage introduced
• The Code of Wages, 2019 introduces a statutory floor wage, which is the minimum wage rate set by the Central Government. This ensures that state governments do not set minimum wages below this floor wage, providing a safeguard for workers.
• Wage to be fixed employment wise
• According to the Code of Wages, minimum wages are to be fixed based on the type of employment and geographical area. This ensures that wages are fair and adequate for different kinds of work and regional cost of living variations.

The correct answer is - Both (A) & (B)

Key Points

• (A) If the classes are of unequal width then the height of the rectangle will be proportional to the ratio of the frequencies to the width of the classes.
• This means that when the class intervals are not the same, the height of the bars in the histogram needs to be adjusted to accurately represent the data.
• The area of each rectangle should correspond to the frequency of the class, so the height of the rectangle is calculated as (frequency / class width).
• Ensures that the visual representation of data is accurate and not misleading.
• (B) If the grouped frequency distribution is not continuous first it is to be converted into continuous distribution and then the histogram is drawn.
• In order to draw a histogram, the frequency distribution must be continuous, meaning there should be no gaps between the class intervals.
• If the data is not in a continuous form, adjustments are made to create continuous intervals, ensuring that the histogram accurately represents the data.
• This step is crucial for creating a correct and meaningful histogram.

Additional Information

• Histogram
• A histogram is a graphical representation of the distribution of numerical data.It is an estimate of the probability distribution of a continuous variable (quantitative variable).
• Histograms are used to depict the frequency distribution of data in a visually interpretable manner.
• Continuous vs. Discrete Data
• Continuous data can take any value within a range (e.g., height, weight, temperature), while discrete data can take only specific values (e.g., number of students, number of cars).
• For histograms, continuous data is preferred because it allows for a more accurate representation of data distribution.

The correct answer is - Frequency polygon

Key Points

• Frequency polygon
• A frequency polygon is a graphical representation of the frequency distribution of a dataset.
• It is constructed by joining the midpoints of the upper sides of adjacent rectangles (bars) in a histogram with straight lines.
• This method provides a clear visualization of the distribution and trends in the data.
• Frequency polygons are useful for comparing multiple distributions on the same graph.

Additional Information

• Frequency curve
• A frequency curve is a smooth curve that represents the frequency distribution of a dataset.
• Unlike the frequency polygon, which uses straight lines, the frequency curve uses a smooth, continuous curve.
• It is often used to approximate the shape of the distribution.
• Frequency line
• This term is not commonly used in statistics and may be confused with the frequency polygon or line graph.
• A line graph typically represents data points connected by straight lines, but it is not specifically used for frequency distributions.
• Frequency chart
• A frequency chart can refer to various types of charts that display frequency distributions, including histograms, bar charts, and pie charts.
• It is a more general term and does not specifically refer to the method of joining midpoints of histogram bars.

The correct answer is - Algebraic sum of the deviations of a set of values from their arithmetic mean is equal to zero.

Key Points

• Algebraic sum of deviations from arithmetic mean

• The arithmetic mean (average) is a measure of central tendency that represents the sum of all values in a data set divided by the number of values.

• By definition, the algebraic sum of the deviations of each value from the arithmetic mean is zero.

• This is because the positive deviations (values above the mean) and negative deviations (values below the mean) cancel each other out.

• Mathematically, if x1,x2,...,xnx1,x2,...,xnx1,x2,...,xn

  are the values in a data set and x¯x¯x¯

  is the arithmetic mean, then ∑ni=1(xi−x¯)=0∑ni=1(xi−x¯)=0∑i=1n(xi−x¯)=0

  .

Additional Information

• Other Options
• Option 1: The statement that the algebraic sum of the deviations is equal to one is incorrect since it disregards the cancellation effect of positive and negative deviations.
• Option 2: The statement that the algebraic sum of the deviations is greater than one is incorrect for the same reason as Option 1.
• Option 4: The statement that the algebraic sum of the deviations is greater than zero is incorrect since the deviations balance out to zero.

The correct answer is - Mean

Key Points

• Mean
• The mean is the arithmetic average of a set of values, calculated by summing all the values and dividing by the number of values.
• It is a measure of central tendency that represents the central point of a data set.
• The sum of the squared deviations of each value from the mean is minimized. This property makes the mean the most efficient measure of central tendency for minimizing the sum of squared deviations.
• This characteristic is vital in statistical methods and analyses, including regression analysis and variance analysis, where minimizing errors is crucial.

Additional Information

• Mode
• The mode is the value that appears most frequently in a data set.
• It is a measure of central tendency used primarily for categorical data or data with repeated values.
• The mode does not minimize the sum of squared deviations; it only indicates the most common value in the data set.
• Median
• The median is the middle value of a data set when the values are arranged in ascending or descending order.
• It is a measure of central tendency that is less affected by outliers and skewed data compared to the mean.
• While the median minimizes the sum of absolute deviations, it does not minimize the sum of squared deviations.
• Zero
• Considering zero as a point of reference for deviations is not a standard measure of central tendency.
• Using zero does not provide meaningful insight into the central tendency of the data set and does not minimize the sum of squared deviations.

The correct answer is - 4 ∶ 1

Key Points

• Given Data
• Average salary of male employees (M) = ₹ 520
• Average salary of female employees (F) = ₹ 420
• Mean salary of all employees = ₹ 500
• Formula and Calculation
• Let the number of male employees be N_m and the number of female employees be N_f.
• Total salary of male employees = 520 × N_m
• Total salary of female employees = 420 × N_f
• According to the mean salary formula:
  

(520N_m + 420N_f) / (N_m + N_f) = 500

• Solving the equation:
  

520N_m + 420N_f = 500(N_m + N_f)

520N_m + 420N_f = 500N_m + 500N_f

20N_m = 80N_f

N_m/N_f = 80/20 = 4/1

Additional Information

• Other Ratios
• 3 ∶ 1 - This ratio would imply a different mean salary. If the ratio was 3:1, the mean salary would not equate to ₹ 500.
• 5 ∶ 2 - Similar to the 3:1 ratio, this would not satisfy the equation derived from the mean salary formula.
• 2 ∶ 3 - This would suggest a higher proportion of female employees, which contradicts the given mean salary.

The correct answer is - Both (A) and (B)

Key Points

• Median
• Statement (A): In case of ungrouped data with an even number of observations, the median is obtained by taking the arithmetic mean of the middle terms after arranging the observations in ascending or descending order.
• For example, in the dataset {2, 3, 5, 8, 9, 12}, which has an even number of observations (6), the middle terms are 5 and 8. The median is calculated as (5+8)/2 = 6.5.
• Statement (B): The median is a positional average.
• It means that the median's value depends on the position of the data points in an ordered list, rather than the actual value of the data points themselves.
• For example, in the ordered dataset {1, 3, 3, 6, 7, 8, 9}, the median is 6, which is the middle position value.

Additional Information

• Median in Different Contexts
• For Ungrouped Data with Odd Number of Observations:
• If the number of observations is odd, the median is the middle value when the data is arranged in ascending or descending order.
• For example, in the dataset {3, 5, 7}, the median is 5.
• Grouped Data:
• For grouped data, the median is found using the median class and applying a specific formula involving the cumulative frequency, class interval, and lower class boundary.
• The formula is Median = L + [(N/2 - CF)/f] * h, where L is the lower boundary of the median class, N is the total number of observations, CF is the cumulative frequency of the class before the median class, f is the frequency of the median class, and h is the class interval.

The correct answer is - Both (A) and (B)

Key Points

• The value of mode is determined by the 'method of grouping' in the following cases:
• If the maximum frequency is repeated: When the highest frequency in the dataset occurs more than once, determining the mode can be complex. The method of grouping helps in identifying the modal class and calculating the precise mode in such scenarios.
• If the maximum frequency occurs in the very beginning or at the end of the distribution: When the highest frequency is located at the extreme ends of the dataset, it can affect the calculation of the mode. The method of grouping assists in adjusting and accurately determining the mode even in such cases.

Additional Information

• Mode:
• The mode is the value that appears most frequently in a data set.
• In a frequency distribution, the mode is the value corresponding to the highest frequency.
• If no value repeats, the dataset is considered to have no mode.
• In cases where multiple values have the same highest frequency, the dataset is bimodal or multimodal.
• Method of Grouping:
• This method is used to determine the mode in grouped frequency distributions.
• It involves creating a frequency distribution table and identifying the modal class.
• The mode is then calculated using the formula for the mode of a grouped frequency distribution.

The correct answer is - Median = 4, Q1 = 3, Q3 = 5

Key Points

• Given data distribution:
• x: 0, 1, 2, 3, 4, 5, 6, 7, 8
• f: 1, 9, 26, 59, 72, 52, 29, 7, 1
• Steps to determine the median, Q1, and Q3:
• Calculate cumulative frequency (cf):
• cf for 0: 1
• cf for 1: 1 + 9 = 10
• cf for 2: 10 + 26 = 36
• cf for 3: 36 + 59 = 95
• cf for 4: 95 + 72 = 167
• cf for 5: 167 + 52 = 219
• cf for 6: 219 + 29 = 248
• cf for 7: 248 + 7 = 255
• cf for 8: 255 + 1 = 256
• Total number of observations (N) = 256
• Median (Q2) is the value at (N/2)th observation:
• Median = value at 128th observation
• Since 95 < 128 ≤ 167, Median = 4
• First quartile (Q1) is the value at (N/4)th observation:
• Q1 = value at 64th observation
• Since 36 < 64 ≤ 95, Q1 = 3
• Third quartile (Q3) is the value at (3N/4)th observation:
• Q3 = value at 192nd observation
• Since 167 < 192 ≤ 219, Q3 = 5

Additional Information

• Understanding Median, Q1, and Q3:
• Median (Q2): The middle value of the dataset when arranged in ascending order. If the dataset size is even, the median is the average of the two middle values.
• First Quartile (Q1): The median of the first half of the dataset. It divides the lowest 25% of data from the remaining 75%.
• Third Quartile (Q3): The median of the second half of the dataset. It divides the lowest 75% of data from the remaining 25%.
• Incorrect Options Brief Overview:
• Option with Median = 3, Q1 = 2, Q3 = 4: Incorrect because it does not align with the cumulative frequency calculations.
• Option with Median = 5, Q1 = 3, Q3 = 6: Incorrect because Median is not 5 according to the cumulative frequency.
• Option with Median = 4, Q1 = 2, Q3 = 5: Incorrect because Q1 is not 2 based on the cumulative frequency.

The correct answer is: Mode.

The mode is the most suitable measure of central tendency for comparing the size of agricultural holdings when the objective is to identify the most frequently occurring size category. This is especially relevant in datasets where there is a concentration of similar-sized holdings, providing insights into the most common holding size.

Key Points

• Suitability of Mode for Agricultural Holdings:
• The mode identifies the most frequent size of agricultural holdings, making it highly relevant in scenarios where a significant number of holdings share the same size.
• It is particularly useful in policy-making and resource allocation by highlighting the typical holding size that is most common.
• Advantages of Mode:
• Mode is unaffected by extreme values or outliers, ensuring a clear representation of the most typical category.
• It provides practical insights for understanding trends in data distributions with distinct peaks or concentrations.
• Limitations of Mean and Median:
• The mean can be skewed by extreme values, making it less representative of the majority in datasets with wide disparities.
• The median provides the central value but does not indicate the most common size, which is often more relevant for agricultural holdings.

Additional Information

• Mode in Skewed Data:
• In distributions where most values cluster around a specific size, the mode effectively represents the dominant group.
• Applications in Agriculture:
• Mode is widely used to analyze agricultural data, particularly in understanding the most common farm sizes and planning support programs accordingly.
• Comparative Insights:
• The mode complements other measures of central tendency, offering unique insights into the distribution’s peak characteristics.

The correct answer is - Standard deviation is the least value root mean square deviation.

Key Points

• Standard deviation
• It is a measure of the amount of variation or dispersion in a set of values.
• It is calculated as the square root of the variance.
• It gives insight into the spread of data points around the mean in a dataset.
• When compared with root mean square deviation (RMSD), standard deviation is generally the least value because RMSD includes both systematic and random errors.
• Root Mean Square Deviation (RMSD)
• It is a measure of the differences between values predicted by a model or an estimator and the actual values observed.
• RMSD is used to measure the accuracy of a model in predicting data points.
• It incorporates both the variance and any bias present in the data.

Additional Information

• Option 1: Standard deviation is the highest value root mean square deviation
• This is incorrect because standard deviation is generally lower than RMSD, not higher.
• Option 3: Standard deviation is not related to root mean square deviation
• This is incorrect as both concepts are measures of dispersion and are related through the inclusion of bias in RMSD.
• Option 4: Standard deviation is always equal to root mean square deviation
• This is incorrect because RMSD typically includes both systematic and random errors, making it higher than the standard deviation which only measures the spread of data points around the mean.

The correct answer is - Variance is independent of change of origin but dependent on change of scale

Key Points

• Variance
• Variance is a measure of the dispersion of a set of data points around their mean value.
• Variance is calculated by taking the average of the squared differences from the mean.
• Mathematically, if XX

is a random variable with mean μμ

, then the variance σ2σ2

is given by σ2=E[(X−μ)2]σ2=E[(X−μ)2]

.

• Variance is independent of change of origin. This means that if you add or subtract a constant to each data point, the variance remains the same.
• However, variance is dependent on the change of scale. If each data point is multiplied by a constant, the variance is multiplied by the square of that constant.

Additional Information

• Change of Origin
• Changing the origin means adding or subtracting a constant from all data points. For example, if you add 5 to every data point, the mean will increase by 5, but the variance remains unaffected.
• Change of Scale
• Changing the scale means multiplying or dividing all data points by a constant. For example, if you multiply every data point by 3, the variance will be multiplied by 32=932=9

.

• This property is because variance measures the average squared deviation from the mean, so any scaling affects the squared deviations.

The correct answer is - Both (A) and (B)

Key Points

• Skewed Distribution
• Skewed distributions occur when data is not symmetrically distributed around the mean.
• In such distributions, the tail on one side of the mean is longer or fatter than the tail on the other side.
• Mean, Mode, and Median
• Statement (A): In a skewed distribution, the mean, mode, and median fall at different points. This is because the presence of outliers or a long tail affects the mean more than the median or mode.
• Quartiles and Median
• Statement (B): In a skewed distribution, quartiles are not equidistant from the median. Quartiles divide the data into four equal parts, but in a skewed distribution, these parts are not evenly spaced around the median.

Additional Information

• Symmetrical Distribution
• In a perfectly symmetrical distribution, such as a normal distribution, the mean, median, and mode are all located at the same point.
• Quartiles are equidistant from the median in a symmetrical distribution.
• Types of Skewness
• Positive Skew (Right Skew): The tail on the right side of the distribution is longer or fatter. The mean is typically greater than the median.
• Negative Skew (Left Skew): The tail on the left side of the distribution is longer or fatter. The mean is typically less than the median.

The correct answer is - Mesokurtic curve

Key Points

• Mesokurtic curve
• A normal curve is referred to as a Mesokurtic curve.
• This curve has a kurtosis (a measure of the "tailedness" of the probability distribution) close to that of a normal distribution, which is zero.
• The shape of a Mesokurtic curve is neither too peaked (leptokurtic) nor too flat (platykurtic), but rather it represents a moderate level of kurtosis.
• In a Mesokurtic distribution, the tails of the distribution are similar to those of a normal distribution, meaning there is an average level of extreme values.

Additional Information

• Platykurtic curve
• A Platykurtic curve is flatter than a normal distribution curve.
• It has negative kurtosis, indicating fewer and less extreme outliers compared to a normal distribution.
• Leptokurtic curve
• A Leptokurtic curve is more peaked than a normal distribution curve.
• It has positive kurtosis, indicating more frequent and extreme outliers compared to a normal distribution.
• Normal Distribution
• The normal distribution, also known as Gaussian distribution, is a continuous probability distribution that is symmetrical around its mean.
• The mean, median, and mode of a normal distribution are all equal.
• It is characterized by the bell-shaped curve which is defined by its mean and standard deviation.

The correct answer is - Negatively skewed

Key Points

• Negatively skewed
• In a negatively skewed distribution, the tail on the left side of the frequency curve is longer or fatter than the right side.
• In this type of distribution, the mean is typically less than the median, which is less than the mode (mean < median < mode).
• The mode being higher than the mean indicates that there are a significant number of higher values in the dataset that pull the mean to the left.
• This causes the frequency curve to skew negatively, meaning the bulk of the data is concentrated on the higher end, with a tail extending to the lower end.

Additional Information

• Symmetric
• A symmetric distribution means the left and right sides of the distribution are mirror images of each other.
• In a symmetric distribution, the mean, median, and mode are all equal.
• Positively skewed
• In a positively skewed distribution, the tail on the right side of the frequency curve is longer or fatter than the left side.
• In this type of distribution, the mean is typically greater than the median, which is greater than the mode (mean > median > mode).
• This is the opposite of a negatively skewed distribution.
• Normal
• A normal distribution is a specific type of symmetric distribution known as the bell curve.
• In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.

The correct answer is - Deterministic Model

Key Points

• Deterministic Model
• A deterministic model is one where the outcome is strictly determined by the conditions under which an experiment is performed.
• In such models, if the initial conditions are known, the future state of the system can be predicted with certainty.
• These models do not involve randomness; the same input will always produce the same output.
• Examples include classical mechanics and many engineering systems.

Additional Information

• Probabilistic Model
• Probabilistic models incorporate randomness and uncertainty into their predictions.
• These models provide probabilities of various outcomes rather than a single deterministic result.
• Examples include quantum mechanics and statistical models in various scientific fields.
• Unpredictable Model
• This is not a standard term in scientific modeling.
• It may refer to systems that are so complex or chaotic that their behavior appears unpredictable.
• Such systems might still follow deterministic rules, but their sensitivity to initial conditions makes long-term prediction practically impossible.
• None of these
• This option implies that none of the provided choices correctly answer the question, which is not the case here.

The correct answer is - B. Pascal and P. Fermat

Key Points

• Blaise Pascal and Pierre de Fermat
• They are considered the founders of the mathematical theory of probability.
• Their correspondence in 1654 on problems related to gambling laid the groundwork for the modern theory of probability.
• Pascal and Fermat's work addressed the "problem of points," which is about dividing stakes in an interrupted game.
• This work is considered the first systematic and rigorous approach to probability theory.

Additional Information

• J. Bernoulli
• Jakob Bernoulli made significant contributions to the field of probability in the late 17th and early 18th centuries.
• His work "Ars Conjectandi," published posthumously in 1713, is one of the most important early works in probability.
• He introduced the "Bernoulli theorem," which is a fundamental concept in the law of large numbers.
• P.S. Laplace
• Pierre-Simon Laplace was a key figure in the development of probability theory in the 18th century.
• His work "Théorie Analytique des Probabilités," published in 1812, is a comprehensive treatise on probability.
• Laplace introduced many concepts and methods that are still used in probability and statistics today.
• De-Moivre
• Abraham de Moivre was an important mathematician in the development of probability theory in the 17th and 18th centuries.
• His work "The Doctrine of Chances," published in 1718, is one of the foundational texts in the field.
• De Moivre is known for the "De Moivre-Laplace theorem," which is a precursor to the central limit theorem.

The correct answer is - Independent events

Key Points

• Independent events
• Events are considered independent if the occurrence or non-occurrence of one event does not affect the occurrence of the other event(s).
• In probability theory, two events A and B are independent if P(A and B) = P(A) * P(B).
• Examples include flipping a coin and rolling a die; the result of the coin flip does not influence the outcome of the die roll.

Additional Information

• Mutually exclusive events
• These are events that cannot happen at the same time. If one event occurs, the other cannot.
• An example is rolling a die: getting a 3 and getting a 5 are mutually exclusive events.
• Favourable events
• These are outcomes that are desired or meet a certain condition in a probability experiment.
• If you are rolling a die and want to get an even number, the favourable outcomes are 2, 4, and 6.

The correct answer is - p = m/n

Key Points

• Probability Theory
• In probability theory, an experiment or a trial is defined as any procedure that can be infinitely repeated and has a well-defined set of possible outcomes.
• The outcomes are considered exhaustive if they cover all possible results of the trial.
• Mutually exclusive outcomes are those that cannot occur simultaneously.
• Equally likely outcomes are those which have the same chance of occurring.
• Calculation of Probability
• The probability (p) of an event E occurring is calculated by dividing the number of favorable outcomes (m) by the total number of possible outcomes (n).
• Therefore, the formula is p = m/n.

Additional Information

• Other Options
• The formula p = mxn is incorrect because it suggests multiplying the number of favorable outcomes by the total number of possible outcomes, which does not provide a meaningful probability value.
• The formula p = n/m is incorrect because it inverts the correct relationship between favorable outcomes and total outcomes, leading to an incorrect calculation of probability.
• The formula p = m is incorrect because it ignores the total number of possible outcomes, which is essential for determining the probability of an event.

The correct answer is: 2/7.

A leap year has 366 days, which means it contains 52 complete weeks (364 days) and two extra days. The specific days of the week for these two extra days determine whether the leap year will have 53 Sundays. The probability of a leap year containing 53 Sundays depends on the possible combinations of these extra days.

Key Points

• Total Weeks in a Leap Year:
• A leap year consists of 366 days, which includes 52 full weeks and 2 extra days.
• Two Extra Days:
• The two extra days can be any of the following combinations:
• Sunday and Monday
• Monday and Tuesday
• Tuesday and Wednesday
• Wednesday and Thursday
• Thursday and Friday
• Friday and Saturday
• Saturday and Sunday
• 53 Sundays in a Leap Year:
• For a leap year to have 53 Sundays, one of the two extra days must be a Sunday.
• Among the 7 possible combinations of extra days, the pairs "Sunday and Monday" and "Saturday and Sunday" include Sunday.
• Probability Calculation:
• There are 2 favorable outcomes ("Sunday and Monday" or "Saturday and Sunday") out of 7 possible outcomes.
• Thus, the probability is 2727

.

Additional Information

• Understanding Leap Years:
• A leap year occurs every 4 years, except for years divisible by 100 but not divisible by 400 (e.g., 1900 was not a leap year, but 2000 was).
• General Case for Non-Leap Years:
• For a regular year (365 days), there is only 1 extra day, and the probability of having 53 Sundays is 1717

.

• Applications:
• This concept is commonly used in probability theory and calendar-related problems.

The correct answer is - (A) The number of trials 'n' is infinite- is not correct

Key Points

• The number of trials 'n' is infinite.
• This statement is not correct for a binomial distribution because the number of trials in a binomial distribution must be finite.
• In a binomial distribution, the experiment is repeated a fixed number of times, denoted as 'n'.
• The assumption of a finite number of trials is crucial to the definition and application of the binomial distribution.

Additional Information

• The trials are independent of each other.
• This is a correct condition for a binomial distribution.
• The outcome of one trial does not affect the outcome of another trial.
• Independence of trials ensures that each trial's result is not influenced by previous outcomes.
• The probability of success 'p' is constant for each trial.
• This is also a correct condition for a binomial distribution.
• The probability of success remains the same for each trial, ensuring consistency in the distribution.
• This constant probability is a key feature that distinguishes the binomial distribution from other distributions.

The correct answer is - (A) and (B)

Key Points

• (A) It is a limiting case of a binomial distribution
• The Poisson distribution can be derived as a limiting case of the binomial distribution as the number of trials goes to infinity while the expected number of successes remains constant.
• When the number of trials (n) is large and the probability of success (p) is small, the binomial distribution B(n, p) can be approximated by the Poisson distribution with parameter λ = np.
• (B) It was discovered by Simeon Dennis Poisson
• The Poisson distribution is named after the French mathematician Simeon Denis Poisson who introduced it in 1837.
• He developed it in the context of studying the number of times a specific event occurs within a fixed interval of time or space.

Additional Information

• (C) The number of trials are indefinitely small
• This statement is incorrect. In a Poisson distribution, the number of trials is typically large, and the focus is on the number of occurrences of an event over a given interval.
• The probability of success for each individual trial is small, not the number of trials.
• (D) The constant probability of success for each trial is indefinitely large
• This statement is incorrect. In a Poisson distribution, the probability of success for each trial is very small, not large.
• The distribution is used to model rare events, where each event has a very low probability of occurring, but there are many opportunities for it to happen.

The correct answer is - Option 2

Key Points

• Normal Distribution
• The graph of a normal distribution is a bell-shaped curve.
• The peak of the bell curve is directly above the mean of the distribution.
• As the standard deviation increases, the curve becomes flatter and wider.
• Explanation of Key Points:
• Bell-Shaped Curve: The normal distribution is often referred to as a "bell curve" because of its shape. The curve is symmetric and has a single peak at the center.
• Mean: The top of the bell curve is located directly above the mean, which is the central point of the distribution. This is a characteristic feature of the normal distribution.
• Standard Deviation: The standard deviation measures the spread of the data around the mean. A larger standard deviation results in a flatter and wider curve, while a smaller standard deviation results in a steeper and narrower curve.

Additional Information

• Other Concepts in Normal Distribution
• Symmetry: The normal distribution is symmetric about its mean. This means that the left and right sides of the curve are mirror images of each other.
• Empirical Rule: Also known as the 68-95-99.7 rule, it states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
• Inflection Points: The points where the curvature changes direction are known as inflection points. For a normal distribution, these occur at one standard deviation away from the mean.

The correct answer is - r(X, Y) = r (U, V)

Key Points

• Correlation Coefficient
• The correlation coefficient between two variables measures the strength and direction of their linear relationship.
• It is denoted by 'r' and ranges from -1 to 1.
• Linear Transformation
• Equations X = a + hU and Y = b + kV represent linear transformations of variables U and V respectively.
• Adding a constant (a, b) or multiplying by a positive constant (h, k) does not change the correlation coefficient between the variables.
• Effect of Constants on Correlation
• Since h > 0 and k > 0, these constants only scale the variables without altering the relationship between them.
• Therefore, the correlation coefficient between X and Y remains the same as that between U and V.

Additional Information

• Correlation Coefficient Properties
• The correlation coefficient is unaffected by changes in the location (mean) or scale (standard deviation) of the variables.
• If X and Y are derived from U and V through linear transformations, their correlation coefficients remain equal.
• Incorrect Options
• Options suggesting r(X, Y) < r(U, V) or r(X, Y) > r(U, V) are incorrect because linear transformations do not affect the correlation coefficient's magnitude or direction.
• Option stating "None of these" is incorrect because r(X, Y) = r(U, V) is a valid statement as explained.

The correct answer is - Only (A) is true.

Key Points

• Statement (A): Two independent variables are always uncorrelated.
• Independence implies no linear relationship between the variables.
• If two variables are independent, the occurrence of one does not affect the occurrence of the other.
• This lack of any linear relationship means that the covariance between the variables is zero.
• As a result, the correlation coefficient, which is a normalized form of covariance, will also be zero.

Additional Information

• Statement (B): Two uncorrelated variables are always independent.
• This statement is incorrect.
• Uncorrelated variables have a correlation coefficient of zero, meaning no linear relationship, but they may still have a nonlinear relationship.
• For example, the variables x and x^2 can be uncorrelated but are clearly not independent.
• Independence is a stronger condition than uncorrelation; it implies no relationship of any form (linear or nonlinear).
• Other Options:
• Option 2: Only (B) is true is incorrect because Statement (B) is false.
• Option 3: Both (A) and (B) are true is incorrect because Statement (B) is false.
• Option 4: None of them is true is incorrect because Statement (A) is true.

The correct answer is - All the three of the above are correct.

Key Points

• Lines of Regression
• (A) It is the line of best fit:
• A regression line represents the best fit line through a set of data points in a scatter plot.
• It minimizes the distance between the actual data points and the predicted data points on the line.
• (B) It is obtained by the principles of least squares:
• The least squares method is a standard approach in regression analysis to determine the best-fitting line.
• It minimizes the sum of the squares of the differences between the observed values and the values predicted by the line.
• (C) It gives the best estimate to the value of one variable for any specific value of another variable:
• The regression line provides the best estimate for the dependent variable based on the value of the independent variable.
• This estimation is particularly useful in predicting outcomes within the range of the observed data.

Additional Information

• Regression Analysis
• Regression analysis is a statistical method used for estimating the relationships among variables.It includes many techniques for modeling and analyzing several variables when the focus is on the relationship between a dependent variable and one or more independent variables.
• Common types of regression analysis include linear regression, multiple regression, and logistic regression.
• Importance of the Least Squares Method
• The least squares method helps in finding the best-fitting line that minimizes the error in prediction.
• This method is widely used due to its simplicity and efficiency in handling data with small sample sizes.
• Applications of Regression Lines
• Regression lines are used in various fields such as economics, finance, biology, and engineering for predictive analysis.
• They help in understanding and predicting trends and making informed decisions based on data.

The correct answer is - When the correlation coefficient is +1 or -1

Key Points

• Correlation Coefficient
• The correlation coefficient measures the strength and direction of a linear relationship between two variables.
• It ranges from -1 to +1.
• A correlation coefficient of +1 indicates a perfect positive linear relationship.
• A correlation coefficient of -1 indicates a perfect negative linear relationship.
• Regression Lines
• Regression lines are used to describe the relationship between dependent and independent variables.
• There are two regression lines: one predicting Y from X and another predicting X from Y.
• When the correlation coefficient is +1 or -1, both regression lines coincide, forming a single line.

Additional Information

• When Correlation Coefficient is 0
• A correlation coefficient of 0 indicates no linear relationship between the variables.
• In this case, the regression lines will be perpendicular to each other.
• When Correlation Coefficient is 0.5 or -0.5
• A correlation coefficient of 0.5 indicates a moderate positive linear relationship.
• A correlation coefficient of -0.5 indicates a moderate negative linear relationship.
• In both cases, the regression lines do not coincide; they intersect at some point.

The correct answer is - Regression coefficients are independent of change of origin and scale

Key Points

• Regression coefficients are independent of change of origin and scale
• This statement is not true because regression coefficients are affected by changes in the scale of the variables. For example, if you multiply all the values of a variable by a constant, the regression coefficient for that variable will also be multiplied by that constant.
• Similarly, changes in the origin (shifting the data) can affect the regression intercept, although the slopes (coefficients) remain unchanged.

Additional Information

• Correlation coefficient is the geometric mean between the regression coefficients
• This statement is true. The correlation coefficient (r) between two variables X and Y is the geometric mean of the regression coefficients of Y on X and X on Y.
• Mathematically, if byxbyx

is the regression coefficient of Y on X and bxybxy

is the regression coefficient of X on Y, then r=byx×bxy−−−−−−−√r=byx×bxy

.

• If one of the regression coefficients is greater than unity, the other must be less than unity
• This statement is true. If byxbyx

must be less than 1, and vice versa. This is because the product of the two regression coefficients is equal to the square of the correlation coefficient, which is always less than or equal to 1.

• Arithmetic mean of the regression coefficients is greater than the correlation coefficient r, provided r > 0
• This statement is true. The arithmetic mean of the regression coefficients is always greater than or equal to the absolute value of the correlation coefficient.
• When r>0r>0

, the mean of the regression coefficients remains greater than the correlation coefficient.

The correct answer is - (C) Correlation co-efficient between X and Y is -0.6.

Key Points

• Regression equations
• The given regression equations are: 8X - 10Y + 66 = 0 and 40X - 18Y - 214 = 0.
• These equations can be solved to find the mean values of X and Y, and the regression coefficients.
• Mean values of X and Y
• The equations can be rearranged to find the mean values of X and Y.
• From the first equation, 8X - 10Y + 66 = 0, we get the mean values of X and Y as 13 and 17 respectively.
• Regression coefficient of Y on X
• The regression coefficient of Y on X can be calculated from the given equations.
• Regression coefficient of Y on X is 0.8.
• Correlation coefficient
• The correlation coefficient between X and Y is not -0.6.
• The correct correlation coefficient can be derived from the regression coefficients, and it turns out to be 0.6, not -0.6.

Additional Information

• Correlation Coefficient Calculation
• The correlation coefficient (r) is related to the regression coefficients (b_yx and b_xy) by the formula r² = b_yx * b_xy.
• Given regression coefficients, b_yx = 0.8 and b_xy can be derived to confirm the sign and value of the correlation coefficient.

The correct answer is - Both (A) and (B) are true.

Key Points

• Multiple correlation
• Multiple correlation relates to the study of joint effect of a group of variables upon a variable not included in the group.
• It measures the strength and direction of the relationship between one dependent variable and two or more independent variables.
• The multiple correlation coefficient (R) ranges from 0 to 1, where 1 indicates a perfect multiple correlation.
• Partial correlation
• Partial correlation relates to the study of only two variables eliminating the linear effect of other variables of the group.
• It measures the degree of association between two random variables, with the effect of a set of controlling random variables removed.
• Partial correlation is useful to understand the direct relationship between two variables after removing the influence of other variables.

Additional Information

• Multiple Correlation Coefficient (R)
• The multiple correlation coefficient (R) is used in the context of multiple regression analysis.
• It indicates how well the independent variables predict the dependent variable.
• Linear Effect in Partial Correlation
• In partial correlation, the linear effect of other variables is removed to better understand the direct relationship between the two main variables.
• This technique helps to isolate the specific influence of each variable in the presence of other variables.

The correct answer is - Positively associated

Key Points

• Positively associated
• If two attributes A and B are positively associated, the occurrence of one attribute increases the likelihood of the occurrence of the other attribute.
• The given condition (AB) > (A)(B)/N indicates that the joint probability of A and B occurring together is greater than what would be expected if they were independent.
• This implies a positive correlation between the two attributes, meaning they tend to occur together more frequently than by chance.

Additional Information

• Negatively associated
• If two attributes are negatively associated, the occurrence of one attribute decreases the likelihood of the occurrence of the other attribute.
• In such cases, the joint probability of A and B occurring together would be less than what would be expected if they were independent.
• Independent of each other
• Two attributes are independent if the occurrence of one attribute does not affect the occurrence of the other attribute.
• This means the joint probability of A and B occurring together would be exactly equal to the product of their individual probabilities, i.e., (AB) = (A)(B)/N.

The correct answer is - Completely associated

Key Points

• Yule's Coefficient of Association
• Yule's Coefficient of Association, denoted as Q, is a measure used in statistics to determine the degree of association between two attributes.
• The value of Q ranges from -1 to +1.
• When Q is +1, it indicates that the two attributes are completely associated.
• Completely Associated
• Complete association means that the presence of one attribute is perfectly linked with the presence of the other attribute.
• For example, if attribute A is present, attribute B will always be present, and vice versa.

Additional Information

• Completely Dissociated
• If Yule's Coefficient of Association is -1, it indicates complete dissociation.
• Complete dissociation means that if one attribute is present, the other attribute is always absent.
• Independent
• If Yule's Coefficient of Association is 0, it indicates that the attributes are independent.
• Independence means that the presence or absence of one attribute does not affect the presence or absence of the other attribute.

The correct answer is - Both (A) and (B) are true

Key Points

• Statistical constants of a population are called parameters
• Parameters are numerical characteristics of a population, such as the mean (average), variance, or standard deviation.
• These values are typically unknown because they describe an entire population, which is often too large to measure completely.
• Parameters are denoted by Greek letters (e.g., μ for population mean, σ for population standard deviation).
• Statistical measures of a sample are called statistics
• Statistics are numerical characteristics of a sample, which is a subset of the population.
• These values are calculated from the sample data and used to make inferences about the population parameters.
• Statistics are typically denoted by Latin letters (e.g., x̄ for sample mean, s for sample standard deviation).

Additional Information

• Parameter vs. Statistic
• A parameter is a fixed measure describing an entire population, while a statistic is a measure describing a sample from the population.
• For example, the average height of all adults in a country is a parameter, while the average height of a sample of 100 adults from that country is a statistic.
• Importance in Statistics
• Understanding the difference between parameters and statistics is crucial for conducting statistical analyses and interpreting the results correctly.
• Statistical inference involves using sample statistics to make estimates or test hypotheses about population parameters.

The correct answer is - (A) and (B) are positively associated

Key Points

• Calculation of association between A and B
• The probability of A occurring, P(A) = (A) / N = 470 / 1000 = 0.47
• The probability of B occurring, P(B) = (B) / N = 620 / 1000 = 0.62
• The joint probability of both A and B occurring, P(A and B) = (AB) / N = 320 / 1000 = 0.32
• If A and B were independent, P(A and B) should be P(A) * P(B) = 0.47 * 0.62 = 0.2914
• Since P(A and B) = 0.32 > 0.2914, A and B are positively associated

Additional Information

• Association Types
• Positive Association: When the occurrence of one event increases the probability of the occurrence of another event.
• Negative Association: When the occurrence of one event decreases the probability of the occurrence of another event.
• Independence: When the occurrence of one event does not affect the probability of the occurrence of another event.
• Incorrect Options
• The events are not negatively associated as P(A and B) > P(A) * P(B).
• The events are not independent as P(A and B) ≠ P(A) * P(B).

The correct answer is - (A), (B), and (C)

Key Points

• Critical values
• (A) It is value of statistic which the critical separates the critical (rejection) region and acceptance region:
• Critical values help determine the threshold at which the null hypothesis is rejected in favor of the alternative hypothesis.
• They are used to define the boundary between the acceptance region (where the null hypothesis is not rejected) and the rejection region (where the null hypothesis is rejected).
• (B) It depends on level of significance:
• The level of significance (alpha, α) determines the probability of rejecting the null hypothesis when it is actually true.
• Common levels of significance are 0.05, 0.01, and 0.10, which correspond to 95%, 99%, and 90% confidence levels, respectively.
• (C) It also depends on the alternative hypothesis:
• The form of the alternative hypothesis (whether it is one-tailed or two-tailed) affects the critical values.
• For a one-tailed test, the critical value is located on one end of the distribution, while for a two-tailed test, the critical values are located on both ends of the distribution.

Additional Information

• Level of significance (α)
• It is the probability of making a Type I error, which occurs when the null hypothesis is true but is incorrectly rejected.
• The choice of α affects the critical value and the width of the rejection region.
• Alternative hypothesis
• The alternative hypothesis represents the outcome that the researcher expects or aims to support.
• It can be one-tailed (indicating a specific direction) or two-tailed (indicating no specific direction but a difference).
• Rejection region
• The rejection region is the range of values for which the null hypothesis is rejected.
• The size and location of the rejection region depend on the level of significance and the form of the alternative hypothesis.

The correct answer is - If modulus of Z is > 1.96, the null hypothesis is rejected at 5% level of significance.

Key Points

• Normal Test (Z-test)
• A Z-test is a type of statistical test that determines if there is a significant difference between sample and population means.
• It assumes that the data follows a normal distribution.
• Critical Value at 5% Level of Significance
• The critical value of Z at a 5% level of significance (two-tailed test) is approximately ±1.96.
• If the calculated Z value is greater than 1.96 or less than -1.96, the null hypothesis is rejected.
• Interpreting the Result
• When |Z| > 1.96, it indicates that the observed data is significantly different from the null hypothesis at the 5% significance level.
• This means there is less than a 5% chance that the observed data is due to random variation alone.

Additional Information

• Option 1
• When |Z| > 3, it is generally at a much lower significance level (0.0027), implying a very strong evidence against the null hypothesis.
• Option 3
• States the opposite of the correct interpretation; if |Z| > 1.96, the null hypothesis is actually rejected.
• Option 4
• At the 1% level of significance, the critical value is ±2.58. If |Z| > 2.58, the null hypothesis is rejected, not not rejected.

The correct answer is - Neither (A) nor (B) is correct.

Key Points

• Unbiased Estimate
• An unbiased estimate is a statistical estimate that, on average, equals the parameter being estimated.
• The unbiasedness property ensures that the expected value of the estimator is equal to the true value of the population parameter.
• Sample Mean
• The sample mean is an unbiased estimator of the population mean.
• This means that the expected value of the sample mean is equal to the population mean.
• Thus, statement (A) is incorrect.
• Sample Variance
• The sample variance, when calculated using the formula with (n-1) in the denominator (Bessel's correction), is an unbiased estimator of the population variance.
• When calculated with n in the denominator, it is biased.
• Thus, statement (B) is correct.

Additional Information

• Understanding Bias
• Bias in an estimator refers to the difference between the expected value of the estimator and the true value of the parameter being estimated.
• If this difference is zero, the estimator is considered unbiased.
• Estimators in Statistics
• Common estimators include the sample mean, sample variance, and sample proportion.
• These are used to infer the corresponding population parameters.

The correct answer is - (A) and (B) are correct.

Key Points

• (A) It is the square of a standard normal variate with one degree of freedom.
• A chi-square variate with one degree of freedom is defined as the square of a standard normal variate.
• Mathematically, if Z is a standard normal variate, then Z^2 follows a chi-square distribution with one degree of freedom.
• (B) Asn (sample size) tends to infinity, the chi square distribution tends to normal distribution.
• This statement aligns with the Central Limit Theorem, which states that the sum of a large number of independent chi-square distributed variables will approximate a normal distribution.
• As the degrees of freedom increase, the chi-square distribution becomes more symmetric and resembles the normal distribution.

Additional Information

• (C) The sum of independent chi square variates is not a chi square variate.
• This statement is incorrect. The sum of independent chi-square variates is itself a chi-square variate.
• If X1, X2, ..., Xk are independent chi-square variates with degrees of freedom ν1, ν2, ..., νk, respectively, then the sum (X1 + X2 + ... + Xk) follows a chi-square distribution with degrees of freedom (ν1 + ν2 + ... + νk).

The correct answer is - All of these are essential.

Key Points

• Essential conditions for the validity of the chi-square test:
• Sample observations should be independent: This means that the observations collected for the chi-square test should not influence each other. Each observation should be collected in such a way that it does not affect any other observation.
• Total frequency should be reasonably large: The chi-square test is based on the approximation of the sampling distribution of the test statistic to the chi-square distribution. This approximation is accurate only when the sample size is large enough, typically around 50 or more.
• No theoretical cell frequency should be less than 5: If any expected cell frequency in the contingency table is less than 5, the chi-square approximation may not be valid. In such cases, the Fisher's Exact Test may be used as an alternative.

Additional Information

• Key concepts related to chi-square test:
• Chi-square distribution: It is a distribution that arises in statistics when one is trying to estimate the variance of a normally distributed population.Degrees of freedom: The chi-square statistic's value depends on the degrees of freedom, which is typically the number of levels of the categorical variables minus one.
• Contingency table: A table often used in chi-square tests to summarize the relationship between several categorical variables.
• Goodness of fit test: A type of chi-square test used to determine if a sample data matches a population with a specific distribution.

The correct answer is - All (A), (B) and (C) are correct

Key Points

• Chi-Square Distribution
• The chi-square distribution is a widely used statistical distribution in hypothesis testing.
• It is particularly useful in tests involving categorical data.
• Goodness of Fit (A)
• The chi-square test for goodness of fit determines if a sample data matches a population with a specific distribution.
• It compares the observed frequencies to the expected frequencies under the null hypothesis.
• Homogeneity of Independent Estimates of Population Correlation Coefficients (B)
• The chi-square test can be used to test the homogeneity of independent estimates of population correlation coefficients.
• It assesses whether different samples have the same correlation coefficient.
• Homogeneity of Independent Estimates of Population Variance (C)
• The chi-square test can be used to test the homogeneity of variances across different samples.
• This is often referred to as Bartlett's test, which uses the chi-square distribution to test the equality of variances.

Additional Information

• Chi-Square Test Applications
• The chi-square test is also used in contingency table analysis to test the independence between categorical variables.
• It can be used in the context of analysis of variance (ANOVA) when assumptions of normality are not met.
• Limitations of the Chi-Square Test
• The chi-square test requires a sufficiently large sample size to ensure the validity of the test.
• It is sensitive to the sample size; very large samples may lead to significant results even for small differences.

The correct answer is - It is used to test the goodness of fit.

Key Points

• t-distribution
• The t-distribution, also known as Student's t-distribution, is used in statistics to estimate population parameters when the sample size is small and the population standard deviation is unknown.
• It is symmetric and bell-shaped, similar to the normal distribution, but has heavier tails, which means it is more prone to producing values that fall far from its mean.
• Applications of t-distribution
• It is used to test the significance of the difference between sample means.
• It is used to test the significance of an observed sample correlation coefficient and sample regression coefficient.
• It is used to test the significance of observed partial and multiple correlation coefficients.

Additional Information

• Goodness of fit test
• The goodness of fit test is typically performed using the chi-square distribution, not the t-distribution.
• This test is used to determine how well a statistical model fits a set of observations.
• It compares the observed values with the expected values to see if there are any significant deviations.

The correct answer is - Only (A) is correct.

Key Points

• Assumptions of Student t-test
• Independent Observations: One of the core assumptions of the Student t-test is that the sample observations are independent. This means that the data points collected from the sample should not influence each other. This assumption ensures the validity of the test results.
• Unknown Population Standard Deviation: The Student t-test is specifically designed for situations where the population standard deviation is unknown. Instead, the sample standard deviation is used as an estimate.

Additional Information

• Incorrect Assumptions
• Known Population Standard Deviation: The assumption that the population standard deviation is known is incorrect for the Student t-test. This assumption applies to the Z-test, not the t-test.
• Both Assumptions: Since the population standard deviation being known is incorrect for the t-test, the option stating both (A) and (B) are correct is also incorrect.

The correct answer is - It is a ratio of two independent chi square variates divided by their respective degrees of freedom.

Key Points

• F-statistic
• The F-statistic is used in the context of the analysis of variance (ANOVA) and regression analysis.
• It is defined as the ratio of two independent chi-square distributed variables divided by their respective degrees of freedom.
• This ratio follows the Snedecor's F distribution, which is named after George W. Snedecor.
• Chi-Square Variates
• In statistics, a chi-square variate is a random variable that has a chi-square distribution.
• A chi-square distribution is a special case of the gamma distribution and is used in various hypothesis testing scenarios.

Additional Information

• Option 2: Product of two independent chi-square variates divided by their respective degrees of freedom
• This is incorrect because the F-statistic is not defined as the product of two chi-square variates.
• The correct definition involves the ratio of two chi-square variates.
• Option 3: Does not follow Snedecor's F distribution
• This is incorrect because the F-statistic does indeed follow Snedecor's F distribution.
• This distribution is crucial for performing ANOVA and regression analyses.
• Option 4: None of these
• This option is incorrect as well, as option 1 correctly defines the F-statistic.

The correct answer is - None of these

Key Points

• F-test is used for testing the significance of an observed multiple correlation coefficient
• The F-test helps determine if the observed multiple correlation coefficient is statistically significant.
• This involves analyzing the relationship between a dependent variable and multiple independent variables.
• F-test is used for testing the significance of an observed sample correlation ratio
• The F-test assesses the significance of the ratio of variances between two samples or groups.
• It is used to check if the variances between the groups are significantly different.
• F-test is used for testing linearity of regression
• The F-test evaluates whether a linear regression model provides a better fit to the data compared to a model with no predictors.
• It is used to test if the relationship between the dependent and independent variables is linear.

Additional Information

• F-test
• The F-test is a statistical test that compares the variances of two populations to determine if they are significantly different.
• It is commonly used in analysis of variance (ANOVA) to test the equality of means for multiple groups.
• The F-test assumes that the data are normally distributed and that the samples have equal variances.
• Multiple Correlation Coefficient
• The multiple correlation coefficient (R) measures the strength of the relationship between one dependent variable and several independent variables.
• It ranges from 0 to 1, where 0 indicates no correlation and 1 indicates perfect correlation.
• Sample Correlation Ratio
• The sample correlation ratio is a measure used in the analysis of variance to indicate the proportion of the variance in the dependent variable that is predictable from the independent variable(s).
• It is also known as the eta squared (η²).
• Linearity of Regression
• Linearity of regression refers to the assumption that the relationship between the dependent and independent variables is linear.
• It means that a change in the independent variable results in a proportional change in the dependent variable.

The correct answer is - (A), (B), and (C) are true.

Key Points

• Statement (A):
• α, the probability of type I error, is indeed called the size of the critical region.
• This is because the critical region defines the set of values that lead to the rejection of the null hypothesis, and α is the probability of making a type I error (false positive).
• Statement (B):
• (1 – β), where β is the probability of making a type II error (false negative), is known as the power of the test.
• The power function indicates the probability of correctly rejecting the null hypothesis when it is false, thus reflecting the test’s ability to detect an effect when there is one.
• Statement (C):
• In quality control terminology, α and β are indeed referred to as producer’s risk and consumer’s risk, respectively.
• Producer’s risk (α) is the risk of rejecting a good batch (false positive), while consumer’s risk (β) is the risk of accepting a bad batch (false negative).

Additional Information

• Type I Error (α):
• This error occurs when the null hypothesis is true, but we incorrectly reject it.
• It is also known as a false positive.
• Type II Error (β):
• This error occurs when the null hypothesis is false, but we fail to reject it.
• It is also known as a false negative.
• Power of a Test:
• The power of a test is the probability that it correctly rejects a false null hypothesis.
• A high power means a lower probability of making a type II error.

The correct answer is - About 21.5 crore

Key Points

• About 21.5 crore
• According to the Periodic Labour Force Survey (PLFS) for the year 2018-19, the workforce employed in agriculture was approximately 21.5 crore.
• This figure reflects the significant portion of the Indian population engaged in the agricultural sector, which remains a crucial part of the economy.
• The agriculture sector in India provides livelihood to a substantial proportion of the rural population and contributes significantly to the country's GDP.

Additional Information

• About 28.7 crore
• This figure is higher than the actual number reported by the PLFS for 2018-19.
• About 25.5 crore
• This figure is also higher than the actual number reported by the PLFS for 2018-19.
• About 30.6 crore
• This figure is significantly higher than the actual number reported by the PLFS for 2018-19.

The correct answer is - 79 lakhs

Key Points

• 79 lakhs
• According to the Periodic Labour Force Survey (PLFS) data, the decline in the number of unemployed persons between the years 2017-18 and 2018-19 was estimated to be around 79 lakhs.
• This figure indicates a significant reduction in unemployment over the specified period.
• The PLFS is a comprehensive survey conducted by the National Statistical Office (NSO) to assess the employment and unemployment situation in India.
• The decline in unemployment can be attributed to various factors, including economic growth, government policies, and initiatives aimed at job creation.

Additional Information

• 70 lakhs
• This figure is incorrect as it underestimates the actual decline in the number of unemployed persons during the specified period.
• 85 lakhs
• This figure is incorrect as it overestimates the actual decline in the number of unemployed persons during the specified period.
• 69 lakhs
• This figure is incorrect as it also underestimates the actual decline in the number of unemployed persons during the specified period.

The correct answer is - 131

Key Points

• India's rank in HDI in 2019
• According to the UNDP Human Development Report 2020, India was ranked 131 out of 189 countries.
• The Human Development Index (HDI) is a composite index measuring average achievement in three basic dimensions of human development—life expectancy, education, and per capita income.
• India's HDI value for 2019 was 0.645, which placed the country in the medium human development category.
• The HDI ranking is used to assess and compare the level of human development across countries.

Additional Information

• Human Development Index (HDI)
• HDI is calculated based on three dimensions:
• Health - measured by life expectancy at birth.
• Education - measured by mean years of schooling for adults aged 25 years and more and expected years of schooling for children of school entering age.
• Standard of living - measured by Gross National Income (GNI) per capita.
• HDI ranks countries into four tiers of human development: very high, high, medium, and low.
• The HDI report also considers inequalities, gender disparities, and multidimensional poverty to provide a broader understanding of human development.
• UNDP Human Development Report 2020
• The report emphasizes the importance of addressing inequalities and enhancing sustainable development.
• It highlights the impacts of the COVID-19 pandemic on human development and the need for innovative policy solutions.
• The report also discusses the concept of planetary pressures–adjusted HDI (PHDI), which incorporates environmental sustainability into the HDI framework.

The correct answer is - Food and Beverage group

Key Points

• Food and Beverage group
• The Food and Beverage group was the major driver of Consumer Price Index for Combined (CPI-C) inflation during the periods of 2019-20 (April-December) and 2020-21 (April-December).
• This group includes essential items such as cereals, pulses, meat, fish, milk, fruits, vegetables, and beverages.
• Food prices have a significant impact on overall inflation due to their substantial weight in the CPI basket.
• Inflation in food prices can be driven by various factors such as supply chain disruptions, seasonal variations, and changes in global food prices.

Additional Information

• Light
• This category generally includes items related to electricity and fuel for lighting.
• While important, the weight of this category in the CPI basket is less compared to the Food and Beverage group.
• Housing
• This category includes rents, maintenance costs, and other housing-related expenses.
• Although housing costs are significant, they did not drive CPI-C inflation as much as food prices during the specified periods.
• Clothing and Footwear
• This group includes expenses on clothing, footwear, and related products.
• Price changes in this category have a smaller impact on overall CPI-C inflation compared to food prices.

The correct answer is - Only (B) is correct.

Key Points

• Consumer Price Index for Industrial Workers (CPI-IW)
• The Consumer Price Index for Industrial Workers (CPI-IW) is compiled and disseminated by the Labour Bureau, which is an attached office of the Ministry of Labour and Employment.
• The CPI-IW is not released on a yearly basis. Instead, it is compiled and released on a monthly basis.
• Therefore, statement (A) is incorrect because the frequency of compilation and dissemination is not yearly but monthly.
• Statement (B) is correct as the CPI-IW is used for regulating dearness allowance paid to Central and State Government employees, among other applications.

Additional Information

• Dearness Allowance (DA)
• Dearness Allowance is a cost of living adjustment allowance paid to government employees, public sector employees (PSE) and pensioners in India, Bangladesh, and Pakistan.
• DA is calculated based on the CPI-IW to counteract the impact of inflation.
• Labour Bureau
• The Labour Bureau, under the Ministry of Labour and Employment, is responsible for the collection, compilation, analysis, and dissemination of statistics on various aspects of labour.
• It conducts surveys and studies to assess the changes in the socio-economic conditions of labour in India.

The correct answer is: 9.1%.

Food inflation refers to the rate at which the prices of food items increase over a specific period, impacting household expenses and the economy. During the April-December period of 2020-21, food inflation in India saw a significant increase, reaching 9.1%, reflecting the impact of various economic and supply-side factors.

Key Points

• Impact of the COVID-19 Pandemic:
• The pandemic disrupted supply chains, leading to shortages and price surges in essential food items.
• Lockdowns and restrictions increased transportation costs, further contributing to food inflation.
• Key Drivers of Food Inflation:
• Increased prices of vegetables, pulses, and cereals due to supply-demand imbalances.
• Higher input costs for agricultural production, such as seeds and fertilizers.
• Government Measures:
• Efforts to stabilize food prices included releasing stocks from buffer reserves and promoting imports of essential commodities.
• Initiatives to support farmers and improve supply chain resilience were implemented to control inflation in the longer term.

Additional Information

• Comparison with Previous Years:
• Food inflation during the April-December period of 2019-20 was comparatively lower, indicating a sharper rise in 2020-21 due to pandemic-induced challenges.
• Policy Implications:
• High food inflation impacts the purchasing power of consumers, particularly low-income groups.
• It prompts monetary policy adjustments by central banks to balance inflation control with economic growth.
• Global Trends:
• Food inflation during this period was not limited to India, as many countries faced similar challenges due to the pandemic.

The correct answer is - 80.96 crores

Key Points

• 80.96 crores
• Under the Pradhan Mantri Garib Kalyan Anna Yojana (PMGKAY), 80.96 crore beneficiaries were provided with additional food grains until November 2020.
• The PMGKAY was an initiative by the Government of India to provide free food grains to the poor and needy during the COVID-19 pandemic.
• This scheme was aimed at ensuring that no one went hungry during the difficult times brought about by the pandemic.
• Beneficiaries received an additional 5 kg of food grains per person per month, over and above their normal entitlement under the National Food Security Act (NFSA).

Additional Information

• Pradhan Mantri Garib Kalyan Anna Yojana (PMGKAY)
• Launched in March 2020 as part of the Pradhan Mantri Garib Kalyan Yojana (PMGKY) to tackle the challenges posed by the COVID-19 pandemic.
• Under this scheme, about 80 crore people covered under the NFSA were eligible for free food grains.
• It was initially announced for three months but later extended multiple times due to the prolonged nature of the pandemic.
• The scheme aimed to ensure food security for the poor and vulnerable sections of society during the unprecedented times of the pandemic.
• National Food Security Act (NFSA)
• The NFSA, also known as the Right to Food Act, was enacted in 2013.
• It aims to provide subsidized food grains to approximately two-thirds of India's 1.3 billion people.
• Under the NFSA, beneficiaries are entitled to receive 5 kg of food grains per person per month at subsidized prices.

The correct answer is: 17.8%.

The Gross Value Added (GVA) by agriculture and allied sectors represents the contribution of these sectors to the overall economy. For the year 2019-20, the agriculture and allied sector accounted for approximately 17.8% of India’s GVA at current prices, highlighting its significance in the country’s economic structure.

Key Points

• Importance of Agriculture in India:
• Agriculture is the backbone of the Indian economy, providing livelihood to a significant portion of the population, especially in rural areas.
• The sector includes activities such as crop production, animal husbandry, forestry, and fisheries.
• Trends in Agricultural Contribution:
• Although the share of agriculture in GVA has been declining over decades due to the growing industrial and services sectors, it remains a crucial part of the economy.
• In 2019-20, the sector showed resilience despite global economic slowdowns, contributing 17.8% to GVA at current prices.
• Government Initiatives:
• Various schemes like PM-KISAN, crop insurance programs, and subsidies for fertilizers and seeds aim to support and enhance the agricultural sector.
• Efforts to modernize agriculture, improve irrigation, and promote sustainable practices are ongoing to boost productivity.

Additional Information

• Comparison with Other Sectors:
• The services sector remains the largest contributor to GVA, followed by industry, with agriculture contributing the smallest share.
• Challenges in Agriculture:
• Issues such as dependence on monsoons, low productivity, and fragmented land holdings affect the sector's growth.
• Future Outlook:
• With increased investments in technology, infrastructure, and market linkages, the sector’s contribution to GVA can be enhanced sustainably.

The correct answer is: 01 April, 2015.

The Faster Adoption and Manufacturing of (Hybrid) and Electric Vehicles in India (FAME India) scheme was launched by the Indian government on 01 April, 2015. This initiative aims to promote the adoption of electric and hybrid vehicles in the country, reducing dependency on fossil fuels and contributing to environmental sustainability.

Key Points

• Objective of the FAME India Scheme:
• The scheme promotes the adoption of electric and hybrid vehicles to reduce vehicular emissions and dependency on fossil fuels.
• It aims to create a market for electric vehicles (EVs) and support the development of necessary infrastructure.
• Phases of FAME India:
• FAME I (2015-2019): Focused on demand creation by providing subsidies for electric vehicles and supporting pilot projects.
• FAME II (2019 onwards): Extended the scheme with increased financial outlay to support EV adoption and infrastructure, such as charging stations.
• Key Features of the Scheme:
• Financial incentives for the purchase of EVs, including two-wheelers, three-wheelers, and public transport vehicles.
• Support for the establishment of charging infrastructure to facilitate widespread EV adoption.
• Encouragement of research and development in EV technology.

Additional Information

• Significance of FAME India:
• Helps in reducing greenhouse gas emissions and combating climate change.
• Contributes to achieving India’s commitment to the Paris Agreement on climate change by promoting sustainable transportation.
• Challenges in Implementation:
• High initial cost of EVs despite subsidies.
• Limited availability of charging infrastructure and range anxiety among users.

The correct answer is - 1.5

Key Points

• Minimum Support Price (MSP)
• The Minimum Support Price (MSP) is a form of market intervention by the Government of India to insure agricultural producers against any sharp fall in farm prices.
• The MSP is announced by the Government at the beginning of the sowing season for certain crops on the basis of the recommendations of the Commission for Agricultural Costs and Prices (CACP).
• Union Budget of 2018-19
• In the Union Budget of 2018-19, the Government of India announced that the MSP for all crops would be kept at a level of 1.5 times the cost of production.
• This decision was aimed at providing a more assured income to farmers and ensuring that they receive a fair price for their produce.
• Cost of Production
• The cost of production includes all the expenses incurred by farmers in growing and harvesting their crops, such as the cost of seeds, fertilizers, labor, and other inputs.
• By setting the MSP at 1.5 times the cost of production, the government aims to cover the cost and provide an additional 50% margin to the farmers.

Additional Information

• Other Options
• 1.25 times – This would provide a lower margin over the cost of production and would not be as beneficial for farmers as the 1.5 times ratio.
• 1.75 times – This option would provide a higher margin than 1.5 times, but it was not the announced policy in the 2018-19 budget.
• 2 times – While this would offer an even higher margin, it was not the figure stated in the Union Budget 2018-19.

The correct answer is - Marine Products

Key Points

• Marine Products
• Marine products have consistently held the largest share in India's agricultural export value from 2015-16 to 2019-20.
• These products include fish, shrimp, crab, and other seafood, which have a high demand in international markets.
• The marine industry in India is supported by a vast coastline and extensive fishing resources, contributing significantly to the export economy.
• Marine exports are facilitated by advancements in aquaculture and sustainable fishing practices.

Additional Information

• Rice Basmati
• Rice Basmati is another significant agricultural export product from India, known for its unique aroma and long grains.
• It is highly valued in markets such as the Middle East, Europe, and the USA.
• However, it did not surpass marine products in terms of export value during the specified period.
• Spice
• India is renowned for its diverse range of spices, including turmeric, pepper, cardamom, and cumin.
• Spices are a crucial part of the agricultural export sector but did not have the largest share compared to marine products during 2015-16 to 2019-20.
• Raw Cotton
• Raw cotton is a significant export commodity for India, with major markets in China, Bangladesh, and Vietnam.
• Although it plays a vital role in the agricultural export sector, its share was not the largest during the mentioned period.

The correct answer is - Southern Region

Key Points

• Southern Region
• The Southern Region of India includes states like Andhra Pradesh, Karnataka, Kerala, Tamil Nadu, and Telangana.
• This region has a well-developed agricultural sector, with a significant contribution to the country's overall agricultural output.
• In 2020-21, the Southern Region received a higher share of agricultural credit compared to other regions.
• The availability of credit in this region has been instrumental in supporting various agricultural activities, including crop cultivation, dairy farming, and horticulture.
• Factors such as better infrastructure, higher literacy rates, and more effective implementation of credit schemes have contributed to the skewed distribution in favor of the Southern Region.

Additional Information

• Eastern Region
• This region includes states like Bihar, Odisha, West Bengal, Jharkhand, and the northeastern states.
• Agricultural credit distribution in this region has been relatively lower due to factors such as smaller landholdings, less developed infrastructure, and lower levels of financial literacy among farmers.
• Western Region
• The Western Region includes states like Maharashtra, Gujarat, Rajasthan, and Goa.
• While this region has a diverse agricultural landscape, the distribution of agricultural credit has not been as high as in the Southern Region.
• Challenges such as water scarcity and varying soil fertility impact agricultural productivity and credit distribution.
• Northern Region
• This region comprises states like Punjab, Haryana, Uttar Pradesh, and Himachal Pradesh.
• Despite having a robust agricultural sector, the Northern Region did not receive as high a share of credit as the Southern Region in 2020-21.
• Factors such as regional disparities and the concentration of credit in specific crops like wheat and rice may influence the distribution.

The correct answer is - Farmer Agreement of Price Assurance and Farm Services Act, 2020

Key Points

• Farmer Agreement of Price Assurance and Farm Services Act, 2020
• This act provides for a national framework on farming agreements that protects and empowers farmers to engage with agri-business firms, processors, wholesalers, exporters, or large retailers for farm services and sale of future farming produce at a mutually agreed remunerative price framework.
• The act seeks to transfer the risk of market unpredictability from the farmer to the sponsor and also enables the farmer to access modern technology and better inputs.
• It also provides for a three-level dispute settlement mechanism: the Conciliation Board, Sub-Divisional Magistrate, and Appellate Authority.

Additional Information

• Farm Produce Trade and Commerce Act, 2020
• This act aims to provide a framework for farmers to engage in intra-state and inter-state trade of their agricultural produce outside the physical premises of markets notified under state Agricultural Produce Market Committees (APMC) laws.
• It promotes barrier-free trade and aims to reduce marketing/transportation costs.
• The Essential Commodities (Amendment) Act, 2020
• This act seeks to remove commodities like cereals, pulses, oilseeds, edible oils, onion, and potatoes from the list of essential commodities.
• It aims to deregulate the production, storage, movement, and distribution of these food commodities.
• The Farmers Promotion and Facilitation Act, 2020
• This appears to be a misnomer or incorrect reference as there is no such act officially recognized by the name "The Farmers Promotion and Facilitation Act, 2020".

The correct answer is - 0.0898

Key Points

• 0.0898
• This figure represents the contribution of the food processing sector to the Gross Value Added (GVA) in manufacturing for the year 2018-19 at 2011-12 prices.
• The food processing sector is a significant part of the manufacturing industry in India, contributing substantially to the economy.
• The data is typically collected and reported by national statistical organizations, reflecting the economic impact of various sectors.

Additional Information

• 0.076
• This figure is lower than the actual contribution of the food processing sector to GVA in manufacturing for 2018-19.
• It may represent an estimate or data from a different year or a different measure within the sector.
• 0.0652
• This figure is significantly lower than the correct value, indicating it is not representative of the 2018-19 contribution.
• It might be a value from an earlier year or a different economic indicator.
• 0.1
• This figure is higher than the actual contribution, suggesting it might be an overestimate or data from another context.
• It could be a projected figure for future years or a value from a broader category within manufacturing.

The correct answer is - Only (B) is correct.

Key Points

• Pradhan Mantri Fasal Bima Yojana (PMFBY)
• Launched in 2016, it aims to provide comprehensive crop insurance coverage to farmers.
• The scheme covers various stages of the crop cycle, including pre-sowing, post-harvest, and localized calamities.
• It includes coverage for prevented sowing, standing crops, and post-harvest losses.
• Statement (A):
• Incorrect: Under PMFBY, individual farm level losses due to localized calamities like cloud burst and natural fire are indeed covered.
• The scheme specifically includes coverage for localized risks to ensure farmers are protected against such perils.
• Statement (B):
• Correct: The average sum insured per hectare has increased significantly from ₹ 15,100 during the pre-PMFBY scheme to ₹ 40,700 under PMFBY.
• This increase demonstrates the enhanced financial protection provided to farmers under the PMFBY scheme.

Additional Information

• Prevented Sowing and Planting Risk
• PMFBY covers risks arising from the inability to sow or plant due to adverse weather conditions.
• Post-Harvest Losses
• The scheme provides coverage for post-harvest losses caused by cyclones, unseasonal rains, and other weather conditions.
• Localized Calamities
• Coverage includes localized events such as hailstorms, landslides, and cloud bursts, which can cause severe damage to crops in specific areas.

The correct answer is - 0.4

Key Points

• The eight core industries
• These industries include coal, crude oil, natural gas, refinery products, fertilizers, steel, cement, and electricity.
• They are critical for the economy as they support infrastructure development and overall industrial production.
• The combined weight of these industries in the Index of Industrial Production (IIP) is approximately 0.4.
• These industries are considered barometers of the industrial sector's health and performance.

Additional Information

• Index of Industrial Production (IIP)
• The IIP is a key indicator of the industrial performance of an economy.The IIP measures the production levels of different sectors within the economy over a period.
• It helps in understanding the growth rate and performance of various industrial sectors.
• Understanding the weights
• Weights in the IIP are assigned based on the relative importance and contribution of each sector to the overall industrial output.
• The higher the weight, the more significant the sector's impact on the overall IIP.

The correct answer is - Electricity, gas, water supply, other utility services

Key Points

• Electricity, gas, water supply, other utility services
• As per the Ministry of Statistics and Programme Implementation (MOSPI) data, the share of the electricity, gas, water supply, and other utility services sector in the Gross Value Added (GVA) has increased during the financial years 2012 to 2021.
• This sector plays a crucial role in the development and functioning of other economic sectors, such as manufacturing, mining, and construction.
• The increased share indicates greater investments and improvements in infrastructure and utility services over the years.
• Such growth is often driven by urbanization, industrialization, and the expansion of residential and commercial spaces requiring reliable utility services.

Additional Information

• Mining
• Mining involves the extraction of minerals and other geological materials from the earth.
• This sector includes activities related to coal mining, metal ore mining, and oil and gas extraction.
• Although important, its share in GVA has seen fluctuations due to changes in global commodity prices, regulatory policies, and environmental concerns.
• Manufacturing
• Manufacturing refers to the production of goods using labor, machines, tools, and chemical or biological processing.
• This sector includes industries such as automotive, textiles, electronics, and pharmaceuticals.
• The share of manufacturing in GVA is influenced by factors such as innovation, labor costs, and international trade dynamics.
• Construction
• Construction encompasses the building of infrastructure such as residential buildings, commercial complexes, roads, bridges, and other physical structures.
• This sector's share in GVA can be affected by government spending on infrastructure projects, economic cycles, and real estate market conditions.

The correct answer is - Start up Intellectual Property Protection

Key Points

• Start up Intellectual Property Protection (SIPP)
• The SIPP scheme is aimed at facilitating the protection of intellectual property rights (IPR) of startups.
• Under this scheme, startups can seek assistance from any empaneled facilitator to file and process their patent, design, or trademark applications.
• The government bears the entire fee of the facilitators for any number of patents, trademarks, or designs that a startup may file.
• This initiative is part of the broader Start-up India action plan, which aims to boost entrepreneurship and innovation by making IPR protection more accessible.

Additional Information

• The Fund of Funds for Startups (FFS)
• Launched by the Government of India to support the growth and development of startups by providing funding through various venture capital funds.
• This initiative aims to boost the availability of capital for startups and drive innovation and entrepreneurship in the country.
• Startup Yatra
• An initiative to spread awareness about the startup ecosystem and opportunities in tier 2 and tier 3 cities.
• It involves organizing boot camps and workshops to inspire and educate aspiring entrepreneurs in these regions.
• Startup Industry Academia Partnership and Incubation
• Focuses on fostering collaboration between the industry and academic institutions to promote research and innovation.
• This initiative aims to create a supportive environment for startups by leveraging the expertise and resources of academia.

The correct answer is - 63

Key Points

• India's Rank in Ease of Doing Business 2020
• According to the Ease of Doing Business Report 2020, India was ranked 63rd for the year 2019.
• This ranking was an improvement from previous years, reflecting significant reforms in various business regulations.
• The Ease of Doing Business index is published by the World Bank, which measures the regulatory environment and ease of establishing and running businesses in different countries.

Additional Information

• Ease of Doing Business Index
• This index is created by the World Bank Group to evaluate the ease of starting and operating a local firm in 190 economies.
• It assesses regulations affecting 10 areas of the life of a business, including starting a business, dealing with construction permits, getting electricity, registering property, getting credit, protecting minority investors, paying taxes, trading across borders, enforcing contracts, and resolving insolvency.
• India's Previous Rankings
• In 2018, India was ranked 77th, reflecting an improvement from 100th in 2017.
• These improvements were a result of various reforms initiated by the Indian government to make it easier to do business in the country.

The correct answer is: 85.16%.

As per the Ministry of Statistics and Programme Implementation (MOSPI) in 2019-20, the service sector contributed a significant 85.16% to the Gross Value Added (GVA) of Delhi. This highlights Delhi’s status as a service-driven economy, with a major focus on sectors like information technology, finance, real estate, and tourism.

Key Points

• Service Sector Dominance in Delhi:
• The service sector is the backbone of Delhi’s economy, contributing 85.16% to its GVA in 2019-20.
• Main contributors include finance, insurance, real estate, professional services, and public administration.
• Factors Driving Service Sector Growth:
• Presence of a large skilled workforce and advanced infrastructure.
• Delhi’s role as the capital city, housing central government offices, multinational corporations, and major service industries.
• Economic Significance:
• The service sector not only drives GVA but also creates substantial employment opportunities.
• It attracts domestic and foreign investments, further boosting economic activities.

Additional Information

• Comparison with National Trends:
• At the national level, the service sector contributes around 55-60% to India’s overall GVA, showing Delhi’s much higher reliance on services.
• Challenges in the Service Sector:
• Dependency on a few key industries makes the economy vulnerable to sector-specific slowdowns.
• Infrastructure and urban congestion pose challenges to sustainable growth.
• Future Outlook:
• Continued investment in technology, innovation, and digital services is expected to further enhance Delhi’s service sector dominance.